Question: What is the value of $\frac{14!}{5!9!}$ ?
Answer: Cancel before multiplying: \begin{align*} \frac{14!}{5!9!}&=\frac{14\cdot13\cdot12\cdot11\cdot10\cdot9!}{5\cdot4\cdot3\cdot2\cdot9!} \\ &= \frac{14 \cdot 13 \cdot 12 \cdot 11 \cdot 10}{5 \cdot 4 \cdot 3 \cdot 2} \\ &= \frac{14 \cdot 13 \cdot 12 \cdot 11}{4 \cdot 3} \\ &= 14 \cdot 13 \cdot 11 \\ &= \boxed{2002} \end{align*}